Answer:
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
There is a 18.03% probability that a randomly selected region had exactly two hits.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this problem we have that:
A total of 545 bombs hit the combined area of 556 regions. So the mean hits per region is:
[tex]P = \frac{545}{556} = 0.9802[/tex]
Assume that we want to find the probability that a randomly selected region had exactly two hits.
This is P(X = 2).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-0.9802}*(0.9802)^{2}}{(2)!} = 0.1803[/tex]
There is a 18.03% probability that a randomly selected region had exactly two hits.
